Finite time stabilization of time-delay nonlinear systems with uncertainty and time-varying delay

In this paper, the problem of finite-time stability and finite-time stabilization for a specific class of dynamical systems with nonlinear functions in the presence time-varying delay and norm-bounded uncertainty terms is investigated. Nonlinear functions are considered to satisfy the Lipchitz conditions. At first, sufficient conditions to guarantee the finite-time stability for time-delay nonlinear system with uncertainties and based on the Lyapunov approach is presented. In the following, sufficient conditions to ensure finite time stabilization the considered system with state feedback are presented. In the proofs of proposed theorems are used from the appropriate Lyapunov-Krasovskii function and newton-Libniz-formula that can reduce the conservative. Also, all of the obtained conditions in this paper are delay-dependent and presented as linear matrix inequalities .Finally, the numerical examples and simulations exhibit the effectiveness of the proposed methods.